Data-controlled variable resistors have been used in place of manually controlled potentiometers in applications, inter alia, requiring periodic or remotely actuated resistance adjustments. For example, one such variable resistor is sold under the name E.sup.2 Pot by Xicor Corporation. The E.sup.2 Pot device has a large number of resistors of different values arranged in parallel and an electronic wiper which becomes conductive with one of a large number of contacts, one of which is associated with each resistance, in order to place a selected one of the resistances in a circuit. Such an arrangement inevitably requires a large amount of space and is also relatively expensive, since a large number of resistors are required to cover a full range of resistances even though only one of the resistors is used at any given time.
Recently, there have been attempts to provide variable resistors which overcome some of the problems associated with the E.sup.2 Pot device. In one such attempt, it has been suggested that a series of resistance circuits may be controlled such that the resistance circuits are combined to produce a large number of resistance values. Each of the circuits in the series includes a resistor having a resistance value that is equal to 2.sup.n R (n being a different integer for each resistance circuit), and that is shunted by a power field-effect transistor (PFET). A particular resistance value for the series is selected by actuating selected ones of the PFETs to effectively short circuit the shunted resistors in the series. Unfortunately, due to the residual impedance of each PFET during its short circuit (or closed) state, selecting a particular resistance value from this prior art arrangement becomes extremely complex when the magnitude of that impedance is equal to or exceeds R.